Conservative Motion Theory – Information I Fredholm–Shannon Entropy and Information Conservation

Kawasaki, Hideyo

Published Nov 19, 2025• 0 citations

Abstract

We introduce the Information Series of Conservative Motion Theory (CMT), providing aFredholm–kernel formulation of Shannon entropy, Fisher information, and mutual information.Information is realized as a spectral invariant of a reflection–positive Fredholm operatorwhose κ → 0+ limit produces a conserved information flux across scales. This yields aunified definition of classical, differential, and quantum information, all arising from a singleoperatorial source.

DOI: 10.5281/zenodo.17648084

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